Existence of solutions for $n^\mathrm{th}$-order nonlinear differential boundary value problems by means of new fixed point theorems

This paper is devoted to prove the existence of one or multiple solutions of a wide range of nonlinear differential boundary value problems. To this end, we obtain some new fixed point theorems for a class of integral operators. We follow the well-known Krasnoselski\u{\i}'s fixed point Theorem together with two fixed point results of Leggett-Williams type. After obtaining a general existence result for a one parameter family of nonlinear differential equations, are proved, as particular cases, existence results for second and fourth order nonlinear boundary value problems.